Dish Network Corp. is in talks to merge with T-Mobile US Inc., people familiar with the matter said, a deal that would accelerate a wave of consolidation across the U.S. media and communications industries.

The two sides are in close agreement about what the combined company would look like, with Dish Chief Executive Charlie Ergen becoming the company’s chairman and his T-Mobile counterpart, John Legere, serving as the combined company’s CEO, the people said.